Most of the available theory of population genetics is based upon the assumption that generations are discrete. One object of our research has been to determine the extent to which the stochastic theory for finite populations remains valid in age-structured populations. Some results have already been obtained and this line of research will be pursued further. Our group and others have done some research on consequences of selection in infinite populations with overlapping generations. Several theories have thus been developed and these seem to differ somewhat in their underlying assumptions. An attempt will be made to obtain an understanding of the extent to which these theories coincide and the ways in which they differ. We propose to do further research on the dynamics and equilibria in populations in which selection takes place by way of competition in groups of a fixed finite size. Further research will be done on a theory of quantitative genetics which integrates multifactorial genetic determination with occurrence of genetically caused variability in viability. finally, there will be a critical examination of the applicability of the ideas of biometrical genetics, emanating from the Birmingham school, and the resulting methodology.